The Cosmological Evolution of the Nucleon Mass and the Electroweak Coupling Constants

Starting from astrophysical indications that the fine structure constant might undergo a small time shift, we discuss the implications of such an effect from the point of view of particle physics. Grand unification implies small time shifts for the nucleon mass, the magnetic moment of the nucleon and the Fermi constant as well. The relative change of the nucleon mass is 123 times larger than the relative change of alpha. Astrophysical constraints indicate that the data from astrophysics are inconsistent, or the errors are largely underestimated. Laboratory measurements using very advanced methods in quantum optics might soon reveal small time shifts of the nucleon mass, the magnetic moment of the nucleon and the fine structure constant, thereby providing not only a breakthrough in the understanding of the unified particle interactions, but also an important crosslink between particle physics and cosmology. partially supported by the Deutsche Forschungsgemeinschaft, DFG-No. FR 412/27-2, email:[email protected] partially supported by the VW-Stiftung Hannover (I-77495). Some recent astrophysical observations suggest that the fine structure constant α might change with cosmological time [1]. If interpreted in the simplest way, the data suggest that α was lower in the past: ∆α/α = (−0.72± 0.18)× 10−5 (1) for a redshift z ≈ 0.5 . . . 3.5 [1]. The idea that certain fundamental constants might not be constant on a cosmological time scale was pioneered by Dirac [2] and Milne [3] who suggested that Newton’s constant G might be time-dependent. In the thirties of the last century P. Jordan suggested that besides gravity also other forces might show a cosmological time-dependence, although he rejected a possible variation in time of the weak interaction strength and of the electron-proton mass ratio [4]. L. Landau suggested in 1955 that a possible time variation of α might be related to the renormalization of the electric charge [5]. More recently, time variations of fundamental constants were discussed in connection to theories based on extra dimensions [6]. In this paper we shall study consequences of a possible time dependence of the fine structure constant, which are expected within the framework of the Standard Model of the elementary particle interactions and of unified theories beyond the Standard Model. In the Standard Model, based on the gauge group SU(3) × SU(2) × U(1), the fine structure constant α is not a basic parameter of the theory, but related to the coupling parameters αi (αi = g 2 i /(4π), where gi are the coupling constant of the SU(3), SU(2) or U(1) gauge interactions)[7]: α(Q = 0) = 1/137.03599976(50) sin θW (Q 2 = m2Z)MS = 0.23117(16) (2) where θW is the electroweak mixing angle. If the three gauge coupling constants are extrapolated to high energy, they come together at an energy of about 10 GeV, as expected, if the QCD gauge group and the electroweak gauge groups are subgroups of a simple gauge group, e.g. SU(5) [8] or SO(10) [9]. Thus the scale of the symmetry breaking of the unifying group determines where the three couplings constants converge. If one takes the idea of grand unification seriously, a small shift in the cosmic time evolution of the electromagnetic coupling constant α would require that the unified coupling constant gun undergoes small time changes as well. Otherwise the grand unification of the three gauge forces would work only at a particular time. Moreover, if one tries to calculate the coupling constant of the grand unified theory, one typically ends up with theories which derive this couplings from the gravitational interaction in more than four dimensions. This is a possible way to achieve a cosmic time dependence of the gauge couplings, and thus in case of a time dependence one should expect, that not